In The Name of Allaah, The Most Merciful, The Bestower of Mercy.
“When two men among the Prophet’s companions met, they would not depart from one another, except after one of them recited to the other:[إِنَّ ٱلۡإِنسَـٰنَ لَفِى خُسۡرٍ ][ وَٱلۡعَصۡرِ] – [By Al-‘Asr (the time). Verily! The human is in loss….(i.e. the full Surah)]. Thereafter one would give Salaam to the other].
After quoting few other narrations and then graded their authenticity, Imaam Al-Albaanee [may Allaah have mercy upon him] said: In these narrations is that one gives Salaam when departing (i.e. one of gives Salaams to the other when departing after meeting). The other affair we benefit (from this report) is that the companions (of the Prophet) held onto this deed and that is the recitation of Surah Al-Asr (i.e. before departing after meeting, one recites Surah Al-Asr to the other and then gives Salaam), because we we (firmly) believe that they were far removed from initiating – in the religion – a newly invented act of worship as a means of getting close to Allaah by way of it; rather the only reason they did this was due to something established by way Allaah’s Messenger [peace and blessings of Allaah be upon him] – either by way of a statement of his, deed or tacit approval. [Silsilah Al-Hadeeth As-Saheehah. Number 2648. Vol 6. pages 307-309]